Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910092422545408 |
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| author | Lescano, Eric |
| author_facet | Lescano, Eric |
| contents | We construct a metric-like formulation of the non-relativistic (NR) limit of bosonic supergravity at the Lagrangian level. This formulation is particularly useful for decomposing relativistic tensors, such as powers of the Riemann tensor, in a manifest covariant form with respect to infinitesimal diffeomorphisms. The construction is purely geometrical and is based on a torsionless connection, mimicking the construction of the relativistic theory. The formulation contains non-vanishing non-metricities, which are associated with the gravitational fields of the theory ($τ_{μν}$, $h_{μν}$, $τ^{μν}$, $h^{μν}$). The non-metricities are fixed by requiring compatibility with the relativistic metric, before taking the NR expansion. We provide a fully covariant decomposition of the relativistic Riemann tensor, Ricci tensor, and scalar curvature. Our results establish an equivalence between the vielbein approach of string Newton--Cartan geometry at the level of the Lagrangian and the proposed construction. We also discuss potential applications, including a pure metric rewriting of the two-derivative finite bosonic supergravity Lagrangian under the NR limit, a powerful simplification in deriving NR bosonic $α'$-corrections and extensions to more general $f(R,Q)$ Newton--Cartan geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03342 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity Lescano, Eric High Energy Physics - Theory General Relativity and Quantum Cosmology We construct a metric-like formulation of the non-relativistic (NR) limit of bosonic supergravity at the Lagrangian level. This formulation is particularly useful for decomposing relativistic tensors, such as powers of the Riemann tensor, in a manifest covariant form with respect to infinitesimal diffeomorphisms. The construction is purely geometrical and is based on a torsionless connection, mimicking the construction of the relativistic theory. The formulation contains non-vanishing non-metricities, which are associated with the gravitational fields of the theory ($τ_{μν}$, $h_{μν}$, $τ^{μν}$, $h^{μν}$). The non-metricities are fixed by requiring compatibility with the relativistic metric, before taking the NR expansion. We provide a fully covariant decomposition of the relativistic Riemann tensor, Ricci tensor, and scalar curvature. Our results establish an equivalence between the vielbein approach of string Newton--Cartan geometry at the level of the Lagrangian and the proposed construction. We also discuss potential applications, including a pure metric rewriting of the two-derivative finite bosonic supergravity Lagrangian under the NR limit, a powerful simplification in deriving NR bosonic $α'$-corrections and extensions to more general $f(R,Q)$ Newton--Cartan geometries. |
| title | Curvatures and Non-metricities in the Non-Relativistic Limit of Bosonic Supergravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2601.03342 |